Question

An 80% confidence interval for a proportion is found to be (0.52, 0.56). What is the margin of error?

a. 0.03
b. 0.02
c. 0.01
d. 0.04

Answer 1

The margin of error for a confidence interval of (0.52, 0.56) is calculated by finding the midpoint or sample proportion, which is 0.54, and then subtracting the lower bound of the interval from it, resulting in 0.02.

Step-by-step explanation:

The margin of error for a confidence interval is the value that is added to and subtracted from the sample proportion to obtain the interval. To calculate the margin of error from the given confidence interval (0.52, 0.56), you take the midpoint of the interval. This is the sample proportion, p'. Subtract the lower bound of the interval from the sample proportion:

Margin of Error (ME) = p' - lower bound

First, find the midpoint (sample proportion):

(0.52 + 0.56) / 2 = 0.54

Then, calculate the margin of error:

0.54 - 0.52 = 0.02

Therefore, the margin of error is 0.02.